Landmark-anchored Rectified Flow: Reducing Velocity-Regression Variance with Training-Free Conditioning

Rectified flow training regresses a velocity field onto its targets, and for small $t$ the irreducible error of this regression approaches the full variance of the training distribution. For any partition of the training set, a measurable share of this variance, 16–63% on the datasets we study, is inter-group, and it encodes only which region of the data a trajectory targets. This share can be computed from the dataset, so the amount by which conditioning lowers the irreducible error is known before training. We propose Landmark-anchored Rectified Flow (LRF), which conditions the flow on a per-group landmark, a training image that represents the group, to lower the irreducible error by its inter-group component. Selecting the landmark requires no second generative model, and the uniform draw over groups makes the trained model an explicit mixture over the landmarks. At matched parameters and training budget, LRF improves FID over a plain rectified flow by 16.3% on ImageNet-256 and 24.4% on CIFAR-10, and reaches the final FID of the baseline with 51–54% fewer training iterations. The explicit mixture gives each sample a known conditioning landmark, and groups can be reweighted without retraining and examined for memorization against held-out data. Code will be released upon acceptance.